Your right about rds, if the voltage on the gate is higher than the gate threshold the fet acts as a resistor, usually a very low value one.
If your just switching a fan on/off you can use a fet just like a power trans, omit the base resistor and put a 1k or so to ground on the gate to keep it pulled down.
You need to worry about gate capacitance and charge etc when your switching at khz or these days 100's of khz.
I cant be bothered with 'official' analogies, I remember them as a comparison to bipolars, drain - collector, gate - base, source - emitter, on a lot of circuits they are laid out in a similar fashion.
You should wear your wrist strap with some fets, they are static sensitive, that said I havent blown one yet.